http://dspace.nbuv.gov.ua:80/handle/123456789/150329 Fri, 10 Apr 2026 10:54:28 GMT 2026-04-10T10:54:28Z http://dspace.nbuv.gov.ua:80/bitstream/id/448075/ http://dspace.nbuv.gov.ua:80/handle/123456789/150329 http://dspace.nbuv.gov.ua:80/handle/123456789/155725 On faithful actions of groups and semigroups by orientation-preserving plane isometries Vorobets, Y. Feitful representations of two generated free groups and free semigroups by orientation-preserving plane isometries constructed. Wed, 01 Jan 2003 00:00:00 GMT http://dspace.nbuv.gov.ua:80/handle/123456789/155725 2003-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/155724 Binary coronas of balleans Protasov, I.V. A ballean B is a set X endowed with some family of subsets of X which are called the balls. We postulate the properties of the family of balls in such a way that a ballean can be considered as an asymptotic counterpart of a uniform topological space. Using slow oscillating functions from X to {0, 1}, we define a zero-dimensional compact space which is called a binary corona of B. We define a class of binary normal ballean and, for every ballean from this class, give an intrinsic characterization of its binary corona. The class of binary normal balleans contains all balleans of graph. We show that a ballean of graph is a projective limit of some sequence of C˘ech-Stone compactifications of discrete spaces. The obtained results witness that a binary corona of balleans can be interpreted as a "generalized space of ends" of ballean. Wed, 01 Jan 2003 00:00:00 GMT http://dspace.nbuv.gov.ua:80/handle/123456789/155724 2003-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/155723 Automorphisms of homogeneous symmetric groups and hierarchomorphisms of rooted trees Lavrenyuk, Y.V.; Sushchansky, V.I. A representation of homogeneous symmetric groups by hierarchomorphisms of spherically homogeneous rooted trees are considered. We show that every automorphism of a homogeneous symmetric (alternating) group is locally inner and that the group of all automorphisms contains Cartesian products of arbitrary finite symmetric groups. The structure of orbits on the boundary of the tree where investigated for the homogeneous symmetric group and for its automorphism group. The automorphism group acts highly transitive on the boundary, and the homogeneous symmetric group acts faithfully on every its orbit. All orbits are dense, the actions of the group on different orbits are isomorphic as permutation groups. Wed, 01 Jan 2003 00:00:00 GMT http://dspace.nbuv.gov.ua:80/handle/123456789/155723 2003-01-01T00:00:00Z http://dspace.nbuv.gov.ua:80/handle/123456789/155721 Post-critically finite self-similar groups Bondarenko, E.; Nekrashevych, V. We describe in terms of automata theory the automatic actions with post-critically finite limit space. We prove that these actions are precisely the actions by bounded automata and that any self-similar action by bounded automata is contracting. Wed, 01 Jan 2003 00:00:00 GMT http://dspace.nbuv.gov.ua:80/handle/123456789/155721 2003-01-01T00:00:00Z